How so? The page you link offers three definitions[1], and all of them require an infinite tape.

You could argue that a stack is missing in my simplified model of the human brain, which would be correct. I used the simple model in allusion to the Chinese room thought experiment which doesn't require anything more than a dictionary.

[1]: https://en.wikipedia.org/wiki/Turing_completeness#Formal_def...

Turing completeness applies to models of computation, not hardware. Otherwise, nothing would be Turing-complete because infinite memory doesn't exist in the real world. Just read the first sentence of what you linked to:

In computability theory, several closely related terms are used to describe the computational power of a computational system (such as an abstract machine or programming language)

Thank you for pointing that out, I was indeed wrong to assume it was used to classify hardware rather than a model.